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Operation on Sets

Read about operation on sets as taught in schools
    A and B are two sets.
  • Complementation
    Complement of sets A and B is denoted as A\B. A\B has the elements of A excluding the common elements of B. The complement of set A is denoted as Ac.
    A\B = {x : x∈A and x∉B}
  • Intersection
    Intersection of sets A and B is the set of all elements that belong to both the sets. It is represented as A∩B.
    A∩B = {x : x∈A and x∈B}
    • A∩B⊆A
    • A∩B⊆B
    • A⊆B ⇒ A∩B = A
    • A∩A = A
    • A∩φ = φ
    • A∩B = B∩A
    • A\B = A∩Bc
  • Union
    Union of sets A and B is the set of all elements that belong to any the sets. It is represented as A∪B.
    A∪B = {x : x∈A or x∈B}
    • A∪A⊆A
    • A∪B = B∪A
    • A∪φ = A
    • If A⊆C and B⊆C = (A∪B)⊆C
  • Distributive Laws:
    1. A∩(B∪C) = (A∩B)∪(A∩C)
    2. A∪(B∩C) = (A∪B)∩(A∪C)
  • De Morgan's Laws:
    1. (B∪C)c = Bc∩Cc
    2. (B∩C)c = Bc∪Cc




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